Automatic Geometric Calibration Using Laser Scanning Reflectometry

ABSTRACT

Systems and methods for calibrating a solid-imaging system ( 10 ) are disclosed. A calibration plate ( 110 ) having a non-scattering surface ( 140 ) with a plurality ( 150 ) of light-scattering fiducial marks ( 156 ) in a periodic array is disposed in the solid-imaging system. The actinic laser beam ( 26 ) is scanned over the fiducial marks, and the scattered light ( 26 S) is detected by a detector ( 130 ) residing above the calibration plate. A computer control system ( 30 ) is configured to control the steering of the light beam and to process the detector signals (SD) so as to measure actual center positions (x A , y A ) of the fiducial marks and perform an interpolation that establishes a calibrated relationship between the angular positions of the mirrors and (x,y) locations at the build plane ( 23 ). The calibrated relationship is then used to steer the laser beam in forming a three-dimensional object ( 50 ).

CLAIM OF PRIORITY

This application claims the benefit of priority under 35 U.S.C. § 119(e)of U.S. Provisional Application Ser. No. 60/957,576, filed on Aug. 23,2007, which application is incorporated by reference herein.

BACKGROUND OF THE INVENTION

1. Field of the Invention

This invention relates to methods and apparatus for calibratingsolid-imaging devices.

2. Technical Background

Solid-imaging devices have been used for rapid prototyping for modelsfor product development, and, more recently for manufacturingoperations. Solid-imaging devices produce three-dimensional objects fromfusible powders or photocurable liquids, typically by exposure toradiation in response to computer control. Data representingcross-sectional layers of a three-dimensional object provide thecomputer with control parameters for programs for automated building ofthe object, typically layer-by-layer. A laser or other source of actinicradiation suitable for solid imaging sequentially irradiates individualthin layers of the build material in response to which the materialtransforms layer-upon-layer into a solid, to create a solid imagingproduct. Example stereolithography apparatus is describe in U.S. Pat.Nos. 4,575,330 and 5,495,328, which patents are incorporated byreference herein.

Solid imaging is sometimes referred to as “rapid prototyping andmanufacturing” and includes such diverse techniques asstereolithography, laser sintering, ink jet printing, and others.Powders, liquids, jettable phase-change materials, and other materialsfor solid imaging are sometimes referred to as “build materials.” Thethree-dimensional objects that solid imaging techniques produce aresometimes called “builds,” “parts,” “objects,” and “solid imagingproducts,” which can be formed as a variety of shapes and sizes.

The builds are usually prepared on surfaces referred to as “build pads”or “build platforms,” which can be raised or lowered to place thesurface of a build into contact with the actinic radiation and the“working surface” or “build plane” or “image plane” where the buildmaterial is exposed.

Despite the variety of devices and methods developed for solid imaging,a number of drawbacks have yet to be resolved in order to make theprocess more efficient and less costly. This includes for example,improving the otherwise complex and tedious alignment steps for aligningthe radiation source and the image plane so that the object is properlyformed.

SUMMARY OF THE INVENTION

The present invention is directed to methods and apparatus forcalibrating a solid-imaging device that forms a three-dimensionalobject, and in particular calibrating the scan of a laser in such adevice over a planar surface. The calibration is performed in a mannerthat accounts for local and global geometric errors so that the laserbeam is accurately and precisely directed when forming thethree-dimensional object.

An aspect of the method involves obtaining a sufficient number ofposition measurements to provide an iterative solution to unknownparameters of a predefined nonlinear model that governs laser scanningkinematics. The position measurements are generated by laser scanning aflat and level calibration plate having a substantially non-scatteringsurface and a periodic array of fiducial marks, which are formed in oron the non-scattering surface and which scatter actinic light. Adetector is arranged above the calibration plate receives the scatteredlight from the fiducial marks as the laser scans over the calibrationplate.

Another aspect of the invention is a method of calibrating asolid-imaging system that forms a three-dimensional object and that hasa mirror-based optical system for generating and steering a light beamhaving an actinic wavelength. The solid-imaging system has an elevatorsystem that movably supports a build platform for building the object.The method includes operably disposing a calibration plate onto thebuild platform. The calibration plate has a periodic array of fiducialmarks formed on a substantially non-scattering background, wherein thefiducial marks are configured to scatter the actinic light. The methodalso includes performing a first scan of the light beam over first andsecond orthogonal rows of fiducial marks and detecting scattered lighttherefrom so as to establish a first coordinate system that is used toestablish first or “theoretical” center positions of the other fiducialmarks in the fiducial mark array. The first and second orthogonal rowsare preferably the center X and Y rows. The method also includes usingthe first coordinate system to perform a second scan of the light beamover at least a portion of the array of fiducial marks and detectingscattered light therefrom so as to measure corresponding centerpositions of the second-scanned fiducial marks. The method furtherincludes using interpolation of the measured center positions and theangular positions of the mirrors to establish a calibrated relationshipbetween mirror angular positions and the (x,y) build plane positions.

The calibration method is substantially immune to thermal environmentalvariables, and the calibration process can typically be completed inless than one hour.

The above-described method meets the calibration criteria of being fast,having no movement of the solid-imaging system (other than the scanningmirrors), and being relatively low cost. The computer controller of thesolid-imaging system is preferably used for the calibration apparatusand is provide with instructions (e.g., software) stored on acomputer-readable medium that recognizes when the laser beam has foundthe center of each fiducial mark via an algorithm that matches thedetector signals associated with the light scattered from the fiducialmark to the known size of the mark and performs an intelligentpattern-matching search. Any change in laser power during the scan hasminimal effect, particularly in example methods that employ multiplescans of the fiducial marks that are then averaged together.

In order to model the system errors as close as possible so that thecalibration is highly accurate and precise, all of the system unknownsmust be iteratively found and reintroduced, so that each set of smallererrors can be identified. A single detector disposed above thecalibration plate provides a central location for receiving data fromthe calibration plate and allows for a complete scan of the plate in amatter of minutes instead of hours. This time savings allows for thecalibration apparatus to obtain a sufficient amount of positionmeasurement information so that the necessary number of iterativecalculations can be performed to provide a calibration that isapproximate the limit of the calibration apparatus's capability.

Additional features and advantages of the invention will be set forth inthe detailed description that follows, and in part will be readilyapparent to those skilled in the art from that description or recognizedby practicing the invention as described herein, including the detaileddescription that follows, the claims, as well as the appended drawings.It is to be understood that both the foregoing general description andthe following detailed description present example embodiments of theinvention, and are intended to provide an overview or framework forunderstanding the nature and character of the invention as it isclaimed. The accompanying drawings are included to provide a furtherunderstanding of the invention, and are incorporated into and constitutea part of this specification. The drawings illustrate variousembodiments of the invention, and together with the detaileddescription, serve to explain the principles and operations thereof.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic diagram of an example embodiment of asolid-imaging system in the form of a stereolithographic system shown inan elevational cross-section;

FIG. 2 is a close-up perspective view of a portion of the optical systemof the system of FIG. 1, that shows an example mirror system along withthe angular coordinates (θ_(X), θ_(Y)) and their relationship to theCartesian coordinates (x, y, z) associated with the build plane;

FIG. 3 is a schematic diagram of the stereolithography system of FIG. 1,and that further includes an example embodiment of the calibrationapparatus according to the present invention that allows for carryingout the calibration methods of the present invention;

FIG. 4 is a plan view of an example embodiment of the calibration plateaccording to the present invention and also shows a close-up view(inset) of an example calibration plate surface that includes a periodicarray of round fiducial marks;

FIG. 5 is a cross-sectional view of an example embodiment of thecalibration plate of FIG. 4 as taken along the line 5-5, along with aclose-up view (inset) of the calibration plate surface;

FIG. 6 is an example embodiment of a 1 foot×1 foot calibration platethat has fiducial marks every 0.25 inch and that includes 48×48=2,304fiducial marks, with the calibration plate surface and the marks shownin reverse contrast for ease of illustration;

FIG. 7A is a schematic plan view of two adjacent round fiducial marks;

FIG. 7B is a schematic plan view of two adjacent hexagonal fiducialmarks;

FIG. 7C is a schematic plan view of two adjacent square fiducial marks;

FIG. 8 a schematic side view of an example embodiment of a calibrationplate similar to that of FIG. 5 but wherein the calibration plateincludes a relatively thick support plate that supports a relative thin“target plate” that includes the fiducial marks;

FIG. 9 is a flow diagram of an example embodiment of a generalcalibration method according to the present invention;

FIGS. 10A-10D are close-up plan views of an example round fiducial markillustrating how the light beam is raster scanned over the fiducial markin two-dimensions to determine a fiducial mark central position;

FIGS. 11A-11C are close-up cross-sectional views of an example fiducialmark and the surrounding non-scattering layer showing the light beamprior to, during, and after passing over the fiducial mark whilescanning the calibration plate; and

FIG. 12 is a schematic diagram of a dual stereolithographic system thatutilizes two calibration plates to perform the dual system calibration.

DETAILED DESCRIPTION OF THE INVENTION

The present invention now will be described more fully hereinafter withreference to the accompanying drawings, in which some, but not allembodiments of the invention are shown. Indeed, the invention may beembodied in many different forms and should not be construed as limitedto the embodiments set forth herein; rather, these embodiments areprovided so that this disclosure will satisfy applicable legalrequirements. The present invention is directed to methods and apparatusfor calibrating solid-imaging devices. An example solid-imaging devicein the form of a stereolithography system is considered below by way ofexample, followed by a description of calibration criteria. These arefollowed by a description of the methods and systems of the presentinvention used to calibrate the stereolithography system.

Example Stereolithography System

FIG. 1 is a schematic diagram of a solid-imaging system in the form of astereolithographic system 10 shown in an elevational cross-section. Aright-handed Cartesian coordinate system is provided for the sake ofreference. System 10 includes a container 20 having an interior region21 (referred as a “build chamber”) that is filled with a UV-curableliquid 22, or the like, to provide a designated working surface or buildplane 23 as defined by the level of the liquid. The term “build plane”as used herein also refers to the location in container 20 where thebuild plane 23 would or could be if liquid 22 were present.

A mirror-based optical system 25 includes a mirror system MS and a lasersource LS or other light beam generator (including but not limited tolaser diodes, light emitting diodes, and the like) configured to providean actinic (i.e., ultraviolet) beam of light 26 that produces a spot(“laser spot”) 27 in the plane of working surface 23. As used herein,“actinic” light includes any and all electromagnetic radiation thatproduces a photochemical reaction in the material that absorbs theelectromagnetic radiation. Such actinic light includes, but is notlimited to, radiation that results in cross-linking of anyradiocrosslinkable material that absorbs the radiation. Optical system25 is configured to move the light beam, such as laser spot 27, acrossbuild plane 23 in order to build an object 50. The movement or“steering” of laser spot 27 over build plane 23 is accomplished byadjusting mirror system MS along with other optical and/or mechanicalelements (not shown) in optical system 26. In an example embodiment,optical system 25 is configured to adjust the size (i.e., diameter orwidth W_(LS); see FIG. 11A) of laser spot 27 to adjust the resolution ofthe laser scan and the resolution of the build process.

In an example embodiment, the steering of laser spot 27 over surface 23is controlled by a computer control system 30. In an example embodiment,computer control system 30 controls such steering based oncomputer-aided design (CAD) data produced by a CAD data generator 32 ina CAD design system or the like. CAD generator 32 in turn is operablyconnected to a computerized CAD data conversion system 34, which isoperably connected to (or is included within) computer control system30. CAD data conversion system 34 is configured to covert the CAD datafrom CAD data generator 32 into a suitable stereolithographic layer dataformat so that the controller can steer laser spot 27 in a manner thatforms object 50.

System 10 includes an elevator system 40 operably connected to computercontrol system 30 (also called a platform surface). Elevator system 40includes a movable build platform 42 that has an upper surface 43. Thebuild platform 42 is operatively connected to an elevator drive 44, suchas a drive screw, piston base, or the like, controlled by the platformdriver 46. The elevator drive 44 selectively moves the build platform 42up and down (i.e., along the Z-direction) via the platform driver 46under the control of computer control system 30.

System 10 further includes a laser leveling system 48 that is operablyconnected to computer control system 30. Laser leveling system 48 isconfigured to generate a laser beam 49 that reflects off of whateversurface is placed therebeneath so as to measure the level of the surfacerelative to a horizontal reference plane.

Build plane 23 of UV-curable liquid 22 is maintained at a constant levelin container 20, and laser spot 27, or other suitable form of reactivestimulation, of sufficient intensity to cure the liquid and convert itto a solid material, is moved across the build plane in a programmedmanner. As UV-curable liquid 22 cures and solid material forms, elevatorplatform 42 (which was initially just below build plane 23) is moveddown from the build plane in a programmed manner via the operation ofelevator driver 44. In this way, the solid material that was initiallyformed is taken below build plane 23 and new liquid 22 is introduced tothe build plane, with or without the assistance of a recoating device orthe like. A portion of this new liquid is, in turn, converted to solidmaterial by actinic light 26 from laser spot 27, and the new materialadhesively connects to the material below it. As the device operates, itproduces the three-dimensional object 50 by step-wise buildup ofintegrated layers (laminae) 52.

This process is continued until the entire three-dimensional object 50is built upon platform surface 43. Object 50 is then removed fromcontainer 20, and the apparatus is ready to produce another object.Another of the same object can then be produced, or some new object canbe made by changing the CAD data provided to computer control system 30.

Optical System

FIG. 2 is a close-up perspective view of a portion of mirror-basedoptical system 25 that shows an example mirror system MS and therelationship between the angular coordinates (θ_(X),θ_(Y)) of the mirrorsystem and the Cartesian coordinates (x,y,z) associated with platformsurface 43. Mirror system MS includes first and second mirrors MX and MYthat are mechanically rotated about respective axes X and Y viarespective mirror drivers (e.g., mirror motors or galvanometers) MDX andMDY, respectively. Mirror motors MDX and MDY are operably connected toand controlled by computer controller 30. Mirror MX controls theX-coordinate at platform surface 43 and mirror MY controls theY-coordinate at the platform surface. Laser beam 26 generated by laserLS is directed to point P=P(x,y,z) by operation of mirrors MX and MYunder the control of mirror motors MDX and MDY, respectively, whereinthe origin at calibration plate surface 132 is taken to be at the centerof Y-dimension mirror MY, at its axis of rotation. Calibration platesurface 132 is at a distance Z away from the center of Y-dimensionmirror MY. The angle θ_(Y) corresponds to the angle of laser beam 26from the vertical in the Y-dimension, and the angle θ_(X) corresponds tothe angle of laser beam 26 from the vertical in the X-dimension.

Considering S to be the distance (spacing) between the center of theY-dimension mirror MY (at its axis of rotation) and the center of theX-dimension mirror MX, and according to well-known relationships in thefield of laser scanning of a planar surface according to this system,one may determine corrected values of the angle of laser beam 26 fromthe vertical in order to irradiate point P as follows:

θ_(Y)=TAN⁻¹(y/Z)

θ_(X)=TAN⁻¹(x/((Z ² +Y ²)^(1/2) +S))

The focal radius FR (not shown) may also be found for this system in theconventional manner, as follows:

FR=[((Z ² +Y ²)^(1/2) +S)² +X ²]^(1/2)

Given these relationships, one may correct for the geometric errorcaused by the planar surface of mirrors MX and MY, and their separationS, for a given distance Z between platform surface 43 and theY-dimension mirror MY.

Calibration Criteria

There are a number of criteria that should be met by a calibrationapparatus for a solid-imaging device. For example, in order to reducethe “shingling” effect of a solidified layer of a formed part, the laserbeam must subtend an angle close to 90 degrees to the build plane. Thisis accomplished by having a large distance from the scanning mirrors tothe build plane. This large working distance hinders the calibrationprocedure because any imperfections in the geometry of the scanningsystem are magnified, such as mirror mounting imperfections, chamberwindow inhomogeneity and non-flatness, mirror shaft warpage, andgalvomotor (i.e., mirror motor) non-parallel mounting.

Furthermore, the theoretical mapping of the angular coordinatesassociated with a pair of scanning mirrors to the build plane has aninherent difficulty that is known to those skilled in the art of laserscanning. The difficulty is that the mapping of the coordinate systemsis nonlinear due to the laser beam not originating from a central pointin space, but rather, from two points of unknown entrance and exitvectors. This configuration draws an arc rather than a line at the buildplane, and creates a mapping error in the form of pincushion distortion.

Another criterion is that there can be no movement of the solid-imagingdevice in any direction or rotation about any axis during datacollection other than by the scanning mirrors. Any movement could beaccounted in the calculations, but it would be limited in accuracy tohow well the movement was detected. Any rotation at all greatly distortsthe error map, and such rotation is difficult to measure at the accuracyrequired.

Also, the exact angle and position of entry of the laser beam to eachmirror, the distance between the mirrors, and the distance from thesecond mirror to the build plane are unknown. The combination of imagingnonlinearity, coupled with the number of unknown parameters and thevarious possible geometric imperfections require that large amounts ofdata are needed to achieve the desire accuracy.

Another criterion is that the calibration must be relatively fast, i.e.,preferably performed in less than one hour, so that any expansion orcontraction of the system due to temperature and humidity over thecourse of the calibration measurement will be negligible. A relatedcriterion is that the relatively large amount of computationalinformation must be processed without significant delay and should be“in-situ” so that a second iteration of the calibration measurement maybe performed without having to re-install any calibration equipment.

Calibration Apparatus

As discussed above, prior to operating system 10 to build object 50, thesystem needs to be calibrated so that laser spot 27 is steered to thedesired object coordinates with a high degree of precision and accuracyso that the intended object is faithfully reproduced.

FIG. 3 is a schematic diagram of the stereolithography system 10 of FIG.1, and which further includes an example embodiment of the calibrationapparatus according to the present invention that allows for carryingout the calibration methods of the present invention. Calibrationapparatus includes a calibration plate 110 having upper and lowersurfaces 112 and 114, and which is arranged with its lower surfaceresting upon platform surface 43. Details of example calibration plates110 are discussed in greater detail below.

Calibration apparatus also includes a photodetector 130 arranged above(i.e., in the +Z direction relative to) calibration plate upper surface112 so as to be out of the way of light beam 26. In an exampleembodiment, photodetector 130 comprises a Si-PIN photodiode having, forexample, a 5.8 mm diameter and a wide wavelength-detection range of 190nm to 1100 nm. Other types of photodetector that are able to detectlight at UV wavelengths (or other wavelengths as required) can also beused, such as GaP-based and GaAsP-based detectors. Photodetector 130generates an electrical detector signal SD in response to detectinglight, as described in greater detail below. In an example embodiment,an optical filter 131 having a bandpass of αλ centered on the actinicwavelength λ₀ is used to limit the detection process to substantiallythe actinic wavelength λ₀.

First Example Calibration Plate

FIG. 4 is a plan view of a first example embodiment of calibration plate110, and FIG. 5 is a cross-sectional view of the calibration plate ofFIG. 4 taken along the line 5-5. Calibration plate 110 includes a rigid,planar substrate 130 having flat upper and lower surfaces 132 and 134.Substrate 130 has a width W_(P), a length L_(P) and a thickness T_(P).An example material for substrate 130 is aluminum. In an exampleembodiment, substrate 130 is an aluminum plate having a generallyuniform thickness T_(P) in the range between about 0.5 inch to about 2inch, and preferably about 0.75 inches. Also in an example embodiment,aluminum substrate upper surface 132 is formed so as have a flatnessFL≦0.005 inch over any 20 inch span. In an example embodiment, aBlanchard grinding process (also called “rotary surface grinding”) isused to achieve the required degree of surface flatness FL. In exampleembodiment, substrate 130 has a width in the range defined by 1foot≦W_(P)≦3 foot, and a length in the range defined by 1 foot≦L_(P)≦4foot. Other substrate sizes (including thicknesses) may also be used,with the size being limited only by the needs of the particular system10, including the need to keep the sag of the substrate to a minimum. Inan example embodiment, the size of substrate 130 defines the size ofcalibration plate 110.

In an example embodiment, calibration plate 110 includes a leveling tab111 that extends outwardly and that has a surface 113 positionedrelative to calibration plate surface 112. Leveling tab 111 ispositioned so that its surface 113 resides underneath laser alignmentsystem 48 and provides a reference surface for the precise leveling ofcalibration plate 110 in system 10.

Calibration plate upper surface 132 is configured so that it does notsubstantially scatter light (i.e., is substantially non-scattering), andpreferably is configured to substantially absorb actinic light 26. Tothis end, in an example embodiment, calibration plate upper surface 132includes a light-absorbing layer 140 formed thereon. In an exampleembodiment, light-absorbing layer 140 is formed via anodization, and ispreferably formed using a photo-anodization. Light-absorbing layer canbe formed using other techniques and/or other materials, such as dyes,paints, plastics, ceramics, etc.

Light-absorbing layer 140 is formed so that it can absorb substantialamounts of actinic light 26 in order to reduce unwanted scattering whenlight spot 27 is scanned over calibration plate 110 between fiducialmarks as described below. In this sense, calibration plate upper surface132 serves as a “dark” or “non-scattering” background.

Calibration plate 110 further includes a periodic array 150 of fiducialmarks 156 formed on calibration plate upper surface 132, e.g., in or onlight-absorbing layer 140. The plurality of fiducial marks 156 areformed so as to be able to scatter actinic light 26. In an exampleembodiment, fiducial marks comprise silver halide formed inlight-absorbing layer 140 during the aforementioned photo-anodizationprocess. FIG. 4 includes an inset that shows a close-up view of anexample light-absorbing layer 140 with round fiducial marks 156. In anexample embodiment, fiducial marks 156 are about the same size as laserspot 27.

In an example embodiment, fiducial marks 156 are formed in aphotosensitive anodized aluminum substrate surface 132 using computernumerically controlled (CNC) milling to create the fiducial marks.Further embodiments provide alternative techniques and/or materials forproviding the plurality of fiducial marks on the substrate surface. Thefiducial marks are associated with the surface of the substrate by beingpositioned on, in, within, or otherwise connected or proximate to thesurface of the substrate.

In an example embodiment, fiducial marks 156 are separated by acenter-to-center distance D_(F) and have a width W_(F). Fiducial marks156 preferably have a center-to-center spacing D_(F) of no greater than1 inch, more preferably no greater than 0.5 inch, and still morepreferably of about 0.25 inch. Fiducial marks 156 preferably have awidth W_(F) of no more than 0.005 inch, more preferably no more than0.004 inch, and still more preferably in the range defined by 0.002inch≦W_(F)≦0.004 inch. The placement accuracy of fiducial mark 156 isprefer-ably equal to or greater than 0.001 inch.

Example calibration plates 110 includes, for example, between 1,000 and20,000 fiducial marks 156. FIG. 6 is an example embodiment of a 1 foot×1foot calibration plate that has fiducial marks spaced apart by distanceD_(F)=0.25 inch and so includes 48×48=2,304 fiducial marks 156. Notethat the calibration plate of FIG. 6 is shown in negative contrast,i.e., the background surface 140 is shown as white and the fiducialmarks are shown as black, for ease of illustration.

A 2 foot×3 foot version of the calibration plate 110 of FIG. 6 includesabout 13,824 fiducial marks 156. However, other numbers of fiducialmarks 156 outside of the above range can be used, depending upon thecalibration plate dimensions, and the spacing D_(F) between the fiducialmarks.

Various shapes can be used for fiducial marks 156, such as circles (FIG.7A), hexagons (FIG. 7B) and squares (FIG. 7C). Other shapes, such ascrosses, box-in-a-box, and other types of polygons or curved shapes canalso be used. Generally, fiducial marks 156 can be any shape that can bescanned with laser spot 70 so as to provide a central (x,y) position ofthe mark using the detected scattered light and an appropriatealgorithm.

Second Example Calibration Plate

The calibration plate 110 described above uses a single thick substrate130, which can be relatively expensive to replace. For example, 2 foot×3foot aluminum substrate 130 having a thickness of 0.75 inch costs about$2,000 once its surface 132 is polished to a high degree of flatness. Ifsurface 132 is scratched or damaged, the entire calibration plate has tobe replaced.

FIG. 8 provides a schematic side view similar to that of FIG. 5 butillustrates a second example embodiment of calibration plate 110 thatincludes substrate 130 as a first support substrate or “support plate”that is substantially inflexible, and a second thin substrate 136 or“target plate” supported by substrate 130 on upper surface 132 and thatis substantially flexible. Substrate 136 has an upper surface 138 onwhich light-absorbing layer 140 and the plurality of fiducial marks 156are formed. In this embodiment, substrate surface 132 need not beanodized. Substrate 136 is preferably aluminum and is relatively thin,e.g., having a thickness in the range from about 0.0015 inch to about0.004 inch, and preferably about 0.002 inch. The thickness of substrate136 is preferably selected so that it can conform to the flatness FL ofsurface 132 of underlying substrate 130. In an example embodiment,substrate 136 is adhered to surface 132 of substrate 130 using alcoholand the resultant surface tension.

An advantage of the two-substrate embodiment of calibration plate 110 isthat if surface 138 that carries array 150 of fiducial marks 156 isdamaged, then only the relatively thin substrate 136 needs to bereplaced at a cost of about $200.

Calibration Method

The method of a preferred embodiment of the present invention is setforth below with reference to flow diagram 200 of FIG. 9. The examplecalibration method can be used before shipment and/or after setup at themanufacturing location. If any mechanical shifting, laser removal orsubstantial laser drift occurs, the calibration procedure should berepeated.

In step 201, calibration plate 110 is inserted into build chamber 21 ofsystem 10 so that calibration plate surface 112 is substantiallyco-planar with build plane 23. As described above, in an exampleembodiment, calibration plate 110 includes a leveling tab 111 used toprecisely level the calibration plate within system 10. The leveling tab111 or other features of the calibration plate 110 may be used to alignor otherwise orient the calibration plate relative to the solid-imagingsystem.

In step 202, light beam 26 is guided to a fiducial mark 156 and a testprofile of the fiducial mark is carried out. This involves, for example,a two-dimensional (2D) raster-scan of the particular fiducial mark 156in the X- and Y-directions.

FIGS. 10A-10D are close-up plan views of an example fiducial mark 156illustrating how light beam 26 is raster scanned over the fiducial markin the X- and Y-directions during the profiling process in order todetermine a “best location” or “center position” 156C for the fiducialmark. Dotted arrow 170 indicates the scan direction of light spot 27.

Data from the 2D raster scan of the selected fiducial mark 156 is thenused to deduce the center position 156C of the fiducial mark, and theproper contrast and black-level for scanning the entire calibrationplate 110. In an example embodiment, center position 156C is determinedby using two different algorithms, such as a centroid algorithm and aGaussian approximation algorithm. Both algorithms must agree as to thedetermination of center position 156C to within a very small margin oferror (e.g., <0.001 inch), or the raster scan of the fiducial mark isrepeated. Other algorithms or approaches for determining center position156C may also be used alone or in combination. The laser power isautomatically adjusted by computer control system 30 for each rasterscan or “profile” in a closed loop, to maximize contrast. In an exampleembodiment, some fiducial marks 156 are “profiled” more than once formeasurement redundancy.

FIGS. 11A-11C are close-up cross-sectional views of an example fiducialmark 156 and light-absorbing layer 140 showing light beam 26 prior to,during, and after passing over the fiducial mark while scanningcalibration plate 110. In FIG. 11B, light spot 27 substantially overlapsfiducial mark 156 to form scattered light 26S, which is detected bydetector 130 (FIG. 3). In between fiducial marks 156, light beam 26 isgenerally absorbed by light-absorbing layer 140 when light spot 27passes between fiducial marks 156 so that essentially no light isscattered to detector 130.

With reference again to FIG. 9 and flow diagram 200, in step 203, theX-axis and Y-axis are identified by performing a first (or initial) beamscan of one row and one column of fiducial marks 156 in the middle ofcalibration plate 110, i.e., a middle row in the X direction (x, 0),then the middle column in the Y direction (0,y). Note that in generalthe first beam scan can be along any two orthogonal rows/columns(“orthogonal rows”) of fiducial marks 156. However, selecting the middlerow and the middle column is preferred in the example embodiments of thepresent invention to establish the origin of the Cartesian coordinatesystem in the middle of calibration plate 110.

The procedure preferably involves using a relatively large laser spotsize to first or initial scan a relatively large area. In an exampleembodiment, laser spot 27 width W_(LS) is about four times the widthW_(F) of the fiducial mark 156 to be found, so that for a fiducial markwidth W_(F)=0.03 inch, the laser spot width W_(LS) is about 0.12 inch.This first, relatively wide scan is performed for each fiducial mark 156for one row and one column, and preferably the middle row and middlecolumn. The use of a relative wide laser spot 27 ensures that fiducialmarks 156 are found within the first scan. After all fiducial marks 156in the middle row and middle column are located, the theoreticalpositions of the remaining fiducial marks 156 of the calibration plate110 are determined by calculation.

This initial scan provides important information that solves for most ofthe theoretical model parameters, including rotation, offset, mirrordistance, second mirror to plane distance, angle of entry, and angle ofexit at origin. These theoretical model parameters are obtained for allfiducial marks by employing known regression analysis techniques usingthe equations described above, and based upon the data collected, forthe middle row and middle column. The regression analysis iteration iscontinued until the RMS error is less than 0.005 inch. This theoreticalmodel allows for quick scans of the remaining fiducial marks 156 in asecond scan, as described below. For example, rather than scanning eachfiducial mark with a relatively large laser spot 27 (e.g., W_(LS)˜0.12inch), as was done for the middle row and middle column as describedabove in connection with the initial scan, the remaining fiducial marksare scanned in the second scan using a narrower laser spot 27, e.g.,W_(LS)=0.040 inch.

By moving mirrors MX and MY in small angular increments dθ_(X) anddθ_(Y) to steer laser beam 26 in corresponding small Cartesianincrements dY and dX, the angular movements of the mirrors versus thedistance traveled is established and the theoretical origin of theinitial coordinate system can be established.

If step 203 is successful, then the rotation, scale, and offset valuesare calculated and are used to create a first coordinate system or“theoretical model” that maps the mirror angular coordinates (θ_(X),θ_(Y)) to the calibration plate X-Y coordinates. This theoretical modeldescribed above is used to predict the “theoretical” positions (x_(T),y_(T)) of the other (i.e., non-scanned) fiducial marks 156. Because ofimperfections in system 10 as a whole prior to calibration, there willgenerally be differences between the theoretical (center) positions(x_(T), y_(T)) and the actual (center) positions (x_(A), y_(A)) of thefiducial marks 156 as measured.

In step 204, at least a substantial portion of, and preferably all offiducial marks 156 of calibration plate 110 are measured in a second (or“measurement”) light beam scan to determine the actual center positions(x_(A), y_(A)) of the scanned fiducial marks 156. This second scan usesthe theoretical positions (XT, YT) to find fiducial marks 156. In anexample embodiment, this full-scan process takes about 20 minutes forabout 10,000 fiducial marks. This allows for the actual and theoreticalcenter positions to be compared and the errors

(δx,δy)=(x _(A) −x _(T) ,y _(A) −y _(T))

between the two measurements to be calculated. This in turn allows forthe identification of local and global errors in the theoretical modelintroduced by imperfections in system 10.

Thus, in step 204, the actual center positions (x_(A), y_(A)) asmeasured in the second scan are provided in a geometric table. Incertain embodiments of the present invention, the geometric tableincludes the scanning-mirror angular coordinate θ_(X) for every 0.25inch increment of the Cartesian coordinate x along the X-axis and ascanning mirror angular coordinate θ_(Y) for every 0.25 inch incrementof the Cartesian coordinate y along the Y-axis

In step 205, the geometric table established in step 204 is used tointerpolate (e.g., using a fifth-order polynomial equation) all scanningmirror angular coordinates (θ_(X), θ_(Y)) to all the calibration plate(x,y) coordinates. This interpolation is created from an equation thatgoverns the complete scan area, and thus is not susceptible to “tiling”errors, such as, local anomalies created by use of only the closestfiducial marks and using a simple averaging algorithm. These“interpolated coordinates” constitute calibrated coordinates (x_(C),y_(C)) that can then be used by computer control system 30 to steerlaser beam 26 when forming object 50. One example embodiment of thepresent invention performs the interpolation with a fourth-order,second-degree polynomial equation to smooth the collected data. Fromthis smoothed data, a traditional bilinear interpolation is performed onthe four closest surrounding data points in the geometric table to givethe correct (i.e., “calibrated”) θ_(X) and θ_(Y).

Accounting for Calibration Plate Errors

It is possible that calibration plate surface 112 can introduce errorsinto the calibration process. Any flatness or rotation errors (e.g.,global and local flatness variations or rotations) will give rise topositional errors in the scanned data. The theoretical flatness of asuspended surface is known to follow a parabolic character and may bemodeled. However, any discrepancy would not be known unless measured,and can change due to temperature and humidity.

Accordingly, in an example embodiment, the calibration method includesthe optional step 206 in which calibration plate 110 is rotated (e.g.,by 45° or 90°) and the first beam scan of the middle X-row and middleY-row is repeated. If calibration plate surface 112 is not perfectlylevel, or if any flatness imperfections exist, or if the periodic array150 of fiducial marks 156 has any rotational errors, then thesediscrepancies would now be rotated as well. If one X-row and one Y-rowof fiducial marks 156 are scanned to determine any flatness and/orrotations errors or offsets, these errors can be accounted for in the(“theoretical”) coordinate system. A similar technique involves loweringor raising calibration plate surface 112 to measure and compensate forany flatness errors.

The Focus Map

Because solid-imaging systems 10 often include a relatively large buildplane 23, mirror-based optical system 25 must dynamically focus laserbeam 26 as it traverses the build plane. Although focal distancemechanics is previously known, any moving part introduces its own offsetand rotation error, thus translating the focused beam spot to adifferent location than intended. Accordingly, in step 207, using theinterpolated coordinate information from step 205, a focus map isgenerated that provides the proper focus for laser beam 26 for a given(x,y) coordinate.

Calibration Verification

In an optional step 208, a visible verification process is carried out.The scanning mirrors use the geometric table to create vectors toirradiate select fiducials 156, which appear to “glow” when irradiateddue to the aforementioned scattered light 26S. The select fiducials 156can be irradiated in a select pattern that allows for a system user toperform visual verification of the calibration.

In another optional step 209 where more than visual calibration proof isrequired or warranted, a light-sensitive material such as black MYLARfilm (not shown) or other polyester film or film of other material isprovided and etched with a select calibration pattern (i.e., fiducialmark irradiation pattern) using laser beam 26 as steered usingcalibrated coordinates. The calibration patterns formed on thelight-sensitive material is then inspected using traditional metrologymethods to confirm the calibration of system 10.

Dual Scanning System

After accommodating all of the above mentioned errors, it is possible toadd another scanning system adjacent thereto so as to increase the buildplane size. FIG. 12 is a schematic diagram of a dual stereolithographicsystem 300 that includes two build chambers operably arranged side byside, and wherein two calibration plates 110 are used to perform thecalibration in the manner described above. This dual stereolithographicsystem 330 may include a computer control system 30 that controlsseparate mirror-based optical systems 25 to move the light beam,generated by a single light beam generator (not shown) or by separatelight beam generators. In certain embodiments the sets of data pointsmay be used to calibrate for the respective build chamber; however, inother embodiments, the sets of data points may be used to stitch thecalibration data together to form a single calibration data set for asingle (combined) build chamber.

Many modifications and other embodiments of the invention set forthherein will come to mind to one skilled in the art to which theinvention pertains having the benefit of the teachings presented in theforegoing descriptions and the associated drawings. Therefore, it is tobe understood that the invention is not to be limited to the specificembodiments disclosed and that modifications and other embodiments areintended to be included within the scope of the appended claims. It isintended that the present invention cover the modifications andvariations of this invention provided they come within the scope of theappended claims and their equivalents. Although specific terms areemployed herein, they are used in a generic and descriptive sense onlyand not for purposes of limitation.

1. A calibration plate for calibrating a solid-imaging system that usesa light beam having an actinic wavelength, the calibration platecomprising: a rigid first substrate having a first surface configured soas not to substantially scatter the light beam; and a plurality offiducial marks associated with the first surface, wherein the fiducialmarks are configured to scatter the light beam.
 2. The calibration plateof claim 1, wherein the first surface comprises a light-absorbingmaterial, and wherein the fiducial marks are formed in or on thelight-absorbing material.
 3. The calibration plate of claim 1, whereinthe first surface is anodized.
 4. The calibration plate of claim 3,wherein the first surface is photo-anodized, and wherein the fiducialmarks comprise silver halide.
 5. The calibration plate of claim 4,wherein the first substrate is formed from aluminum and defines athickness generally between about 0.5 inch about ˜2 inches, and whereinthe first surface has a flatness FL≦0.005 inch as measured over any 20inch span.
 6. The calibration plate of claim 1, wherein the fiducialmarks comprise one of round dots, square dots and hexagonal dots, thedots having a diameter of about 0.030 inch and center-to-center spacingof about 0.25 inch.
 7. The calibration plate of claim 1, wherein thefirst substrate has a thickness in the range between about 0.5 inch andabout 2 inch, and wherein the first surface has a flatness FL≦0.005 inchas measured over any 20 inch span, the calibration plate furthercomprising: a second substrate having a second surface and disposed atopthe first surface and having a thickness such that the second substratesubstantially conforms to the first surface flatness, wherein the secondsurface is substantially non-scattering, and wherein the fiducial marksare formed on the substantially non-scattering second surface.
 8. Thecalibration plate of claim 7, wherein the second substrate has athickness in the range from about 0.0015 inch to about 0.004 inch. 9.The calibration plate of claim 7, wherein the second surface issubstantially light-absorbing.
 10. The calibration plate of claim 9,wherein the second surface is anodized.
 11. The calibration plate ofclaim 10, wherein the second surface is photo-anodized, and wherein thefiducial marks comprise silver halide.
 12. A calibration apparatus forcalibrating a solid-imaging system that has a mirror-based opticalsystem having mirrors with adjustable angular positions for steering alight beam having an actinic wavelength and that has a build plane thatis selectively exposed by the light beam to create an object, thecalibration apparatus comprising: a calibration plate comprising anon-scattering surface and a plurality of fiducial marks operablydisposed proximate the build plane, wherein the non-scattering surfacedoes not substantially scatter the light beam and the fiducial marks areconfigured to scatter the light beam; a photodetector arranged above thecalibration plate so as to detect scattered light from the fiducialmarks and generate detector signals in response thereto; and a controlsystem configured to control the steering of the light beam and toprocess the detector signals so as to measure center positions of thefiducial marks and perform an interpolation that establishes arelationship between the angular positions of the mirrors and (x,y)locations at the build plane.
 13. A calibration apparatus of claim 12,wherein the calibration plate comprises: a first substrate having athickness in the range between about 0.5 inch and about 2 inch andhaving a first surface with a flatness FL≦0.005 inch as measured overany 20 inch span; and a second substrate having a second surface anddisposed atop the first surface and having a thickness such that thesecond substrate substantially conforms to the first surface flatness,wherein the second surface is substantially non-scattering, and whereinthe fiducial marks are formed on the substantially non-scattering secondsurface.
 14. A solid-imaging system for forming a three-dimensionalobject and that includes a calibration apparatus arranged therein,comprising: a light beam generator that generates a light beam ofactinic wavelength; mirrors arranged to receive the light beam and thatare angularly adjustable to steer the light beam; an elevator systemthat movably supports a build platform that has an associated buildplane; a calibration plate selectively disposed generally on the buildplane, the calibration plate having a generally non-light-scatteringsurface with a plurality of fiducial marks formed thereon that areconfigured to scatter the light beam; a photodetector arranged above thecalibration plate and relative to the mirror-based optical system so asto detect the scattered light beam from the fiducial marks and generatedetector signals in response thereto when the light beam passes over thefiducial marks; and a control system configured to process the detectorsignals so as to measure center positions of the fiducial marks andperform an interpolation that establishes a calibrated relationshipbetween the angular positions of the mirrors and (x,y) locations at thebuild plane and steer the light beam using the calibrated relationship.15. The solid-imaging system of claim 14, wherein the calibration plateincludes a light-absorbing surface.
 16. The solid-imaging system ofclaim 14, wherein the calibration plate includes a photo-anodizedsurface with silver-halide fiducial marks formed thereon.
 17. Thesolid-imaging system of claim 14, wherein the calibration platecomprises: a first aluminum substrate having a thickness in the rangebetween about 0.5 inch and about 2 inch, and having a first substratesurface with a flatness FL≦0.005 inch per 20 inch span; and a secondsubstrate disposed atop the first substrate surface and having athickness such that the second substrate substantially conforms to thefirst surface flatness, wherein the second substrate defines thesubstantially non-light-scattering surface, and wherein the fiducialmarks are formed in or on the second substrate surface.
 18. Thesolid-imaging system of claim 17, wherein the second substrate has athickness in the range from about 0.0015 inch to about 0.004 inch. 19.The solid-imaging system of claim 14, wherein the fiducial marks areformed as either round dots, square dots, or hexagonal dots, the dotshaving a diameter of about 0.030 inch with a center-to-center spacing ofabout 0.25 inch.
 20. The solid-imaging system of claim 14, wherein thecalibration plate has a width W_(P) in the range defined by 1foot≦W_(P)≦3 foot, and a length L_(P) in the range defined by 1foot≦L_(P)≦4 foot.